Publications
Partners
He is just the second British player to reach the last four in Paris in the Open era (since 1968) after Tim Henman did so in 2004, and it sets him up for a crack at defending champion Rafael Nadal in Friday's semi-finals.
With Roger Federer and Novak Djokovic contesting the other semi-final, it will be the first time since the 2006 French Open that the top four seeds are into the last four in a Grand Slam event.
Murray, who only completed his five-sets, fourth round win over Serbia's Victor Troicki 24 hours earlier, again started sluggishly, as he tested out the right ankle he injured against Michael Berrer in the fourth round.
The 31-year-old Chela, who had lost six straight times against the Scot, including in the last two years at Roland Garros, jumped out into a 4-1 lead with two breaks of serve before the fourth seed started to get into his stride.
The 24-year-old Murray saved two sets points to get to 5-4 and then on cue broke Chela's serve again to get level.
The set went to a tie-break which saw Chela win the first point against serve before Murray went on a run of five straight points to eventually take it 7/2 after which he headed off court for a comfort break.
On the resumption Murray grabbed another break and he looked totally in control as he smoothly moved 4-1 up with Chela looking for, but not finding, any answers to the Scot's domination.
A change of shirt from white and blue to black and yellow seemed to bring some brief respite for the South American as he broke the Murray serve to get to 4-2, but it did not last long as Murray replied in kind in the next game.
Inexplicably, serving for the set at 5-2 up, Murray again seemed to lose his focus allowing Chela to win three games in a row, with two service breaks, to draw level at 5-5.
The Scot buckled down though to take the next two games for a two sets lead.
He then broke Chela yet again to start the third and this time he raced away to victory keeping alive his hopes of finally winning a Grand Slam title after losing in three finals.
But to do so he will first have to get past Nadal, who he has never beaten on clay.
Results at Roland Garros on Wednesday:
Men
Quarter-finals
Rafael Nadal (1), Spain, def. Robin Soderling (5), Sweden, 6-4, 6-1, 7-6 (3).
Andy Murray (4), Britain, def. Juan Ignacio Chela, Argentina, 7-6 (2), 7-5, 6-2.
Women
Quarter-finals
Maria Sharapova (7), Russia, def. Andrea Petkovic (15), Germany, 6-0, 6-3.
Li Na (6), China, def. Victoria Azarenka (4), Belarus, 7-5, 6-2.
